Effect of quantization of vibrations on the structural properties of crystals

TL;DR

This paper investigates how quantizing vibrational modes affects crystal structures, comparing various approximation methods and highlighting the importance of quantum effects, especially in hydrogen-bonded systems, through first-principles calculations.

Contribution

It introduces a comprehensive methodology for analyzing vibrational quantization effects in crystals, evaluating multiple approximation techniques against exact solutions.

Findings

VSCF is highly accurate for vibrational mode correlations.

QHA works well for covalent but not hydrogen-bonded systems.

Zero-point energy causes non-analytic behavior in hydrogen bonds.

Abstract

We study the structural effects produced by the quantization of vibrational degrees of freedom in periodic crystals at zero temperature. To this end we introduce a methodology based on mapping a suitable subspace of the vibrational manifold and solving the Schroedinger equation in it. A number of increasingly accurate approximations ranging from the quasi-harmonic approximation (QHA) to the vibrational self-consistent field (VSCF) method and the exact solution are described. A thorough analysis of the approximations is presented for model monoatomic and hydrogen-bonded chains, and results are presented for a linear HF chain where the potential energy surface is obtained via first-principles electronic structure calculations. We focus on quantum nuclear effects on the lattice constant, and show that the VSCF is an excellent approximation, meaning that correlation between modes is not extremely important. The QHA is excellent for covalently-bonded, mildly anharmonic systems, but it fails for hydrogen-bonded ones. In the latter, the zero-point energy exhibits a non-analytic behavior at the lattice constant where the H-atoms center, which leads to a spurious secondary minimum in the quantum-corrected energy curve. An inexpensive anharmonic appoximation of non-interacting modes appears to produce rather good results for hydrogen-bonded chains, for small system sizes. However, it converges to the incorrect QHA results for increasing size. Isotope effects are studied for the first-principles HF chain. We show how the lattice constant and the HF distance increase with decreasing mass, and how the QHA proves to be insufficient to reproduce this behavior.